Question

Question 1: Motion on a horizontal plane [25]
On a horizontal plane, a force of 58 N in the horizontal direction acts on an object of mass 10 kg.

(1) Find the magnitude of the normal force N acting on the object from the plane.

(2) Neglecting friction, find the magnitude of the acceleration a of the object.

(3) Assuming that the coefficient of friction between the object and the plane is 0.50, find the magnitude of the acceleration a of the object.

Question 2: Motion on an inclined plane

An object of mass 10 kg starts from rest and slides down an inclined plane making an angle θ = 30◦ with the horizontal.

(1) Find the magnitude of the normal force N acting on the object from the incline.

(2) Neglecting friction, find the magnitude of the acceleration a of the object.

(3) Assuming that the coefficient of friction between the object and the incline is 0.50, find the magnitude of the acceleration a of the object. [5]

Question 3: Work-energy theorem

On a frictionless horizontal plane, a constant force F in the horizontal direction acts upon an object of mass m = 2.00 kg which is moving in the same direction with vi = 5.0 m/s. When its speed reaches vf = 10.0 m/s, the force F ceases to act.

(1) Find the kinetic energy Ki of the object before the acceleration.

(2) Find the kinetic energy Kf of the object after the acceleration.

(3) Find the work W done by F.

(4) The object travels the distance L = 3.0 m while F is acting. Find the magnitude of F .

Question 4: Motion due to gravity [25] hiAn object of mass m = 1.0 kg is falling because of gravity, and has a
speedofvi =10m/sataheightofhi =10mfromtheground. Take
the reference point to be at the ground level.

(1) Find the potential energy Ui of the object at hi = 10 m.

(2) Find the kinetic energy Ki of the object at hi = 10 m.

(3) Find the potential energy Uf of the object at a height of hf = 5.0 m from the ground.

(4) Find the speed vf of the object at hf = 5.0 m.

Question 5: Motion due to a restoring force of a spring

vi = 0

A horizontal spring is lying on a frictionless table. One end of the
spring is fixed and the other end is connected to an object of mass
m = 1.00 kg. The spring is compressed by a distance of 8.00 cm from
its natural length, and then released from rest. The spring constant is k = 250 N/m. Take the reference point to be the position of the object
at which the spring is in the natural length.

(1) Find the magnitude of the restoring force F acting on the object when the spring is compressed by 8.00 cm.

(2) Find the potential energy Ui stored when the spring is compressed by 8.00 cm.

(3) Find the work W done by the spring in restoring itself to its natural length.

(4) Find the speed vf of the object at the instant when the spring returns to its natural length.

Question 6: Conservation law of momentum

A cannon of mass M is at rest on a frictionless horizontal plane, and a cannonball of mass m is loaded. When the cannonball is shot horizontally from the cannon with a muzzle speed v, the cannon recoils with a speed of V .

(1) Express the muzzle speed v in terms of M, m and V .

(2)SupposethatM=2380kg,m=28.0kgandV =1.80m/s. a. Determine the value of the muzzle speed v.

b. Find the work W done for the cannonball during the shooting process.

c. It takes ∆t = 0.420 s for the cannonball to travel in the cannon barrel from rest. Find the magnitude of the average force F acting on the cannonball.

Answer 1